Solve for $x$ and $y$ using elimination. ${-x-4y = -49}$ ${x-5y = -41}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-9y = -90$ $\dfrac{-9y}{{-9}} = \dfrac{-90}{{-9}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-x-4y = -49}\thinspace$ to find $x$ ${-x - 4}{(10)}{= -49}$ $-x-40 = -49$ $-x-40{+40} = -49{+40}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 10}$ into $\thinspace {x-5y = -41}\thinspace$ and get the same answer for $x$ : ${x - 5}{(10)}{= -41}$ ${x = 9}$